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Unformatted text preview: Biostatistics course Part 16 Lineal regression Dr. Sc. Nicolas Padilla Raygoza Department of Nursing and Obstetrics Division Health Sciences and Engineering Campus Celaya Salvatierra University of Guanajuato Biosketch Medical Doctor by University Autonomous of Guadalajara. Pediatrician by the Mexican Council of Certification on Pediatrics. Postgraduate Diploma on Epidemiology, London School of Hygiene and Tropical Medicine, University of London. Master Sciences with aim in Epidemiology, Atlantic International University. Doctorate Sciences with aim in Epidemiology, Atlantic International University. Associated Professor B, Department of Nursing and Obstetrics, Division of Health Sciences and Engineering, University of Guanajuato, Campus Celaya Salvatierra, Mexico. padillawarm@gmail.com Competencies The reader will know how plot a regression line He (she) will apply a hypothesis test on regression line He (she) will know how make ANOVA analysis Introduction When one thinks that one variable depends on the other, it must quantify the relationship between them. In doing so, we can estimate the value of a variable, if we know the value of the other. This method is called regression. Lineal regression Scatter plot show the relationship between age and systolic arterial tension from 37 women. Arterial tension change with age. Re la tio n sh ip b e tw e e n a g e a n d systolic a rte ria l te n sion 50 100 150 200 250 0 50 100 A g e (ye ar s ) Systolic arteria tension (mm Hg) Plotting a regression line Our objective is to draw a line that best describes the relationship between X and Y. You can draw a line with a ruler, that joint the points, but is unlikely to get an unique line and each gives a different description of the relationship between X and Y. Relationship betw een age and hemoglobin 5 10 15 20 0 20 40 60 80 Age (years) Hemoglobin (gr/dl) Each vertical distance is the difference between the observed value for the dependent variable (in the yaxis) and the value of the line for the corresponding value of the xaxis. The vertical distance between the observed and the layout is known as residual. We call each of the residuals e1. R elationship betw een age and hem oglobin 5 10 15 20 0 20 40 60 80 Age (ye a rs) Hemoglobin (gr/dl) Residuals e 1 Plotting a regression line The line that better describe the data is best known as a regression line. Gives an estimate of the average value of y for each x value. In general, we say that is a regression of y on x. We may think of the regression line as a line joining the mean values for each value of x. 5 10 15 20 0 5 10 15 Plotting a regression line The mathematical expression for the regression line equation is: y = + x where is the intersection of the line with the y axis, and is the slope of the line....
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This note was uploaded on 02/23/2012 for the course STAT 312 taught by Professor Staff during the Fall '11 term at Rutgers.
 Fall '11
 Staff
 Statistics, Biostatistics

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